# User:Brian P. Josey/Notebook/Junior Lab/2010/09/13

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## Speed of Light

SJK 21:47, 3 October 2010 (EDT)
21:47, 3 October 2010 (EDT)
This is an excellent primary notebook. Great work, keep it up!

For this experiment, my partner, Kirstin, and I measured the speed of light. The speed of light is one of the most fundamental physical constants, and the fastest speed at which anything can travel. To do this, we shot light from an light emitting diode (LED) down a long cardboard tube to a photomultiplier tube (PMT). This PMT then measures the incoming light and converts it into a signal. We then measured the differences in the signals on the oscilloscope to find the time that it takes for light to travel a given length down the tube. From the measured time for a given distance, we were able to calculate the speed through linear regression, as explained in more detail in the procedure and results sections below. From our data, we were able to successfully measure the speed of light as 31.0 ± 0.5 cm/ns. The accepted value for the speed of light is 29.98 cm/ns in a vacuum.(SJK:How about in our air? Does it matter?)

### Equipment

SJK 20:41, 3 October 2010 (EDT)
20:41, 3 October 2010 (EDT)
Your equipment and setup sections are excellent.
LED used in experiment.
Chassis containing some of the components.
The set up in its final form with all the attached wires.

In addition to the cardboard tube, LED light, and PMT, we had several pieces of equipment that we used in this experiment. They were:

• Tektronix TDS 1012 Oscilloscope
• Bertan Model 215 High voltage power supply
• Ortec TAC/SCA Module (Model 567)
• Harrison Laboratories Power Supply (Model 6207A, 160V, 0.2A)
• Canberra Delay Module (Model 2058)

There are a couple of safety concerns with the experiment. The first is that both of the power supplies generate a significant voltage and current, so shock is a major concern, and once the power supplies were turned on and connected, touching any frayed wires, or the back and underside of the chassis could result in shock. There was also a risk of damaging the PMT by exposing it to too much light; once the PMT was on, it could not be removed from the tube or the ambient light would overload it and ruin it. Even removing the LED from the tube could result in too much light reaching the PMT as is to be avoided.

### Set Up

The PMT was already placed in the cardboard tube at one end, while the LED was attached to a series of meter sticks taped together at the other end. These meter sticks are used to measure how far the LED is from the PMT at any given time. With the PMT and LED already in place, we began to connect all of the other components into place. To do this we inserted the Betran power supply, Ortec TAC and Canberra Delay Module into the chassis and secured them with thumbscrews. Then by using BNC cables, we connected the other components. The A connection of the PMT was connected to the top input of the delay module, while the output of the delay module was connected to a T-splitter. One part of the splitter was connected to the channel 1 input on the oscilloscope, while the other was connected to the stop input on the TAC. We connected the start input on the TAC to the LED, and we connected the power cable of the LED to the Harrison power supply. Finally, we connected the output of TAC to channel 2 on the oscilloscope, and the "-HV" port on the PMT to the Bertan power supply completing all of the wiring.

We then adjusted the settings on our set up for the experiment. On the Bertan power supply, we set the polarity to negative, voltage to 2000 V and the offset to 400 V. On the delay module, we set the delay to 20 ns, and the Harrison power supply to 190 V. On the TAC, we set the range to 100 ns, the multiplier to 1, the output switch to to "Out" and the start and stop switches to "Anti".

### Procedure, Data and Analysis

SJK 21:45, 3 October 2010 (EDT)
21:45, 3 October 2010 (EDT)
I think I am missing whether you record what voltage level you tried to keep the PMT signal at. A picture of that on the scope would help too.
Signals generated on the oscilloscope

In order to measure the speed of light, we measured the delay in the signals between the emitting of light by the LED and its detection by the PMT. To do this, the two signals were fed into the TAC, and the the delay between the two was converted into a voltage that could be read on the oscilloscope. However, because the signal in the wires is not instantaneous, we had to induce a delay on the signal from the PMT due to the fact that the wires connecting it to the oscilloscope were significantly shorter than the ones connected to the LED. This delay, 20 ns on the delay module, was used to match the signals, and remove any systematic error induced by the cables.

To get the data, we pulled the LED to a distance of 1 m away from the PMT. At this point we then twisted the PMT so that its signal, the spike pointing downward in the picture, was at its greatest magnitude. Then we measured the magnitude of signal form the TAC, the lower signal in the picture that levels out at a point. This second signal was the time the light traveled converted into a voltage, from our settings, we determined that 1 V on the signal corresponded to 10 ns. We pushed the LED closer the PMT in 20 cm steps. After moving the LED we rotated the PMT so that its signal on the oscilloscope was at the same magnitude for each step. This worked to counter the time walk phenomena, described below. After adjusting the PMT, we then measured the voltage, of the second signal to find the elapsed time. The data is summarized below in the table.

key=0AjJAt7upwcA4dGR1aVd5ZjhRSWRCM3M1aVhwU2I2OGc width=900 height=400

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Data and best fit line
SJK 21:20, 3 October 2010 (EDT)
21:20, 3 October 2010 (EDT)
It's a little unclear whether you fit time versus distance or distance versus time, since you don't talk about a reciprocal or how you propagate the uncertainty. It's great that you include the spreadsheet, because I can figure it out from there. It's a little tough, still, since I for some reason can't download or edit the spreadsheet. That is an aspect of Google doc, I think--don't know if there's a solution as of now, besides giving the world edit access. This is just a minor point, very good description of what you did.

Besides that, what other ways could you analyze your data? Is it appropriate to average the five trials? What if there were some kind of drift? What if you fit each run individually and then get five slopes? If you do think it appropriate to average the runs, can you include uncertainties in your means that are useful for fitting? These are questions for the future that we will talk about in lecture.

We were successful in taking 5 sets of data with points spread out a distance of 20 cm between each point. To measure the speed of light, we plotted the average values of time traveled, column C above starting in row 8, to our distances. From this plot we also plotted a best fit line whose slope was our value for the speed of light. Plot to the right. Using linear regression, we found the speed as 31.0 ± 0.5 cm/ns. The accepted value, taken from Wikipedia is 29.98 cm/ns. This means that our measured value was more than two standard deviations away from the accepted value. Because our data was consistent, but inaccurate, it implies that there was a systematic error throughout our experiment.

There are multiple possibilities for a error in this experiment. There could have been error in the way we measured on the oscilloscope, the wires could have induced an error, or time walk could have delayed altered the measured value.

Oscilloscope error One of the first things we noticed when we began to take measurements was that the oscilloscope would fluctuate wildly in its display of the signals. This is probably the result of extra background noise in the signal, and made it difficult to find the where the signals were at their maximum. To counter this, we averaged the signals on the oscilloscope to make it easier to read. This could have changed the values for the time traveled, and thrown off our data. However, because we were looking for the average in the signal for out measurement in the first place, it is unlikely that this factor had a major influence on the outcome of out data.

Length of Cables As I mentioned above, we had to delay the signal from the PMT to account for the travel time of the signal along the wires. Had we been measuring a slow speed, the delay in the signals would be too slight to significantly alter our measurements. However, the speed of an electric signal in a wire is comparable to the speed of light, and could have had a real affect on our measurements. Unfortunately for us, we were unable to measure the length of each cable and the speed at which the signal traveled in it, so our applied delay was the best value we could find for our data. It is highly likely that the source of our error relates to the wires and the delay in the signals.

Time Walk As we varied the distance between the PMT and LED, the height and width of the PMT signal also varied. The TAC is set to go off at a specified voltage and changed the distance, this voltage would occur at different time in the signals path. To account for this, we rotated the PMT to polarize the light and return the signal to its initial state. By repeating this procedure with every step, we worked to remove the error induced by the time walk effect.

## Conclusions

In this experiment, my partner and I were able to successfully measure the speed of light, however it was off from the accepted value by a significant margin. Our measured value was 31.0 ± 0.5 cm/ns, while the accepted value is 29.98 cm/ns, which is more than two standard deviations away from our value. Because of this margin of error, it is likely that there was some source of systematic error in our data. While there were many possible sources in the error in the experiment, our error is most likely from the travel time in the wires the signal took between our instruments and the oscilloscope. If we were to repeat this experiment, we would most likely spend more time carefully finding the source of systematic error, and working with the delay in our signal.SJK 21:41, 3 October 2010 (EDT)
21:41, 3 October 2010 (EDT)
As mentioned on your summary page, I'm not convinced about wire length problem -- see that page for discussion.

## Acknowledgments

Once again, I worked with Kirstin on this experiment, and recieved some help and advice from both Katie and Koch. We used Dr. Gold's manual to set up the experiment, and as the primary source for the procedure. I also used both Paul Klimov's and Alexandra Andrego's notebooks as guides and references.SJK 21:43, 3 October 2010 (EDT)
21:43, 3 October 2010 (EDT)
Good acknowledgments